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Single-Station Sigma Using NGA-West2 Data
SSHAC Level 3 Southwestern U.S. Ground Motion Characterization WS-1, March 21, 2013
Oakland, CA
Linda Al Atik
Resource Expert
Residual Components
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es e esB W
eB : Between-event (inter-event) residual for earthquake e
esW : Within-event (intra-event) residual at station s for earthquake e
2 2
: Between-event standard deviation
: Within-event standard deviation
Strasser et al. (2009)
Single-Station Sigma: Approach
• Given multiple recordings of GM at an individual site, S, allows estimating the systematic site effects, , and removing them from the GM variability: Single-Station Sigma
• represents the systematic deviation of the observed amplification at this site from the median amplification predicted by the model
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2 SS S
2 SS S
Single-Station Sigma: Approach (cont’d)
• : systematic deviation of the observed amplification at this site from the median amplification at this site predicted by the model
• :Single-station within-event standard deviation
• :Single-station standard deviation
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2es es sWS W S S
2 SS S
SS
2 2
SS SS
SS
Application to PSHA
• Removing the site-to-site residual from the GM variability leads to a reduced aleatory variability
• However, the median GM at the SITE needs to be estimated:
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( ) ( , , ,...) 2es es e es s e esln Y T M R T S S B WS
If site-specific knowledge is limited, use of single-station sigma SHOULD be accompanied with an INCREASE in
epistemic uncertainty
Terminology
Ergodic Partially Non-Ergodic
Within-event residual, Single-station within-event residual,
Within-event standard deviation, Single-station within-event standard deviation,
Total standard deviation, Single-station standard deviation,
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esW 2es es sWS W S S
SS
2 2 2 2
SS SS
Al Atik et al. (2010)
Data Needs
• Minimum of 5 recordings per earthquake in order to compute a reliable event term,
• Minimum of 5 recordings per site in order to compute the average site-to-site residual,
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eB
2 sS S
NGA-West2 Dataset
• CA SMM and global LM dataset:
– 21,539 recordings from 600 eqks
– 163 recordings with Sa = -999 eliminated
– 3 recordings missing magnitude eliminated
– 34 recordings missing distance measures eliminated
– 12 recordings missing station info eliminated
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21,327 recordings from 578 eqks at 4,096 stations
NGA-West2 Dataset with Periods
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0
5000
10000
15000
20000
25000
0.01 0.1 1 10
Nb
of
Re
cord
ings
Period (sec)
NGA-West2: Data Distribution
• CA: 15,264 recs
• Taiwan: 1,986 recs
• Japan: 1,946 recs
• China: 1,332 recs
• Italy: 333 recs
• NZ: 217 recs
• Other (Alaska, Iran, Greece, Turkey, …): 249 recs
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3
4
5
6
7
8
0 200 400 600 800 1000 1200 1400 1600
Mag
nit
ud
e
Rrup (km)
California Japan China Italy New Zealand Taiwan
21,327 recordings from 578 eqks of 2.99 ≤ M ≤ 7.9
NGA-West2: Data Distribution (cont’d)
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Total number of earthquakes: 578 408 earthquakes with 5 or more recordings
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50
100
150
200
250
300
350
1 2 3 4 5 6 7 8 9 10 > 10
Fre
qu
en
cy
Nb. of Recordings per Eqk
NGA-West2: Data Distribution (cont’d)
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For events with minimum of 5 recordings: Total number of stations: 4,012 838 stations have 5 recordings or more 399 stations have 10 recordings or more
0
200
400
600
800
1000
1200
1400
1600
1800
1 2 3 4 5 6 7 8 9 10 > 10
Fre
qu
en
cy
Nb. of Recordings per Station
NGA-West2: Data Distribution (cont’d)
Minimum of 5 recs per eqk and per station:
15,592 recs from 364 eqks at 838 stations
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3
4
5
6
7
8
0 200 400 600 800 1000 1200 1400 1600
Mag
nit
ud
e
Rrup (km)
California Taiwan China Italy
Region Nrecs CA 13,162
Taiwan 1,339
China 1,076
Italy 15
NGA-West2: Data Distribution (cont’d)
Minimum of 5 recs per eqk and per station:
15,592 recs from 364 eqks at 838 stations
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0
1000
2000
3000
4000
5000
6000
7000
50 150 250 500 700 900 1100 > 1200
Fre
qu
en
cy o
f R
ecs
Vs30 (m/sec)
Preliminary PhiSS Results: NGA-West2
Using preliminary AS13 within-event residuals:
– Minimum of 3 recs per eqk
– 15,619 recs from 326 eqks at 3,164 stations
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Region Nrecs CA 12,025
Japan 1,700
Taiwan 1,535
Italy 175
New Zealand 72
China 48
Iran + Turkey 43
Others 21 3
4
5
6
7
8
0 50 100 150 200 250 300 350 400
Mag
nit
ud
e
Rrup (km)
CA Japan Taiwan Other
AS13 Dataset at PGA
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0
200
400
600
800
1000
1200
1400
1 2 3 4 5 6 7 8 9 10 >10
Fre
qu
en
cy
Nb. of Recordings per Station
Total number of stations: 3,164 675 stations have 5 recordings or more 322 stations have 10 recordings or more
AS13 Dataset at PGA (cont’d)
Minimum of 5 recs per station: 11,188 recs
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Region Nrecs CA 10,123
Taiwan 1,049
Italy 16
3
4
5
6
7
8
0 50 100 150 200 250 300 350 400
Mag
nit
ud
e
Rrup (km)
CA Taiwan Italy
AS13 Dataset at PGA (cont’d)
Minimum of 5 recs per station: 11,188 recs
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0
500
1000
1500
2000
2500
3000
3500
4000
4500
50 150 250 500 700 900 1100 > 1200
Freq
uen
cy o
f Rec
s
Vs30 (m/sec)
Preliminary Results
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0.3
0.4
0.5
0.6
0.7
0.8
0.01 0.1 1 10
Stan
dar
d D
evi
atio
n
Period (sec)
Phi PhiSS
0.3
0.4
0.5
0.6
0.7
0.8
0.01 0.1 1 10
Stan
dar
d D
evi
atio
n
Period (sec)
PhiSS All PhiSS-CA PhiSS-Taiwan
CA PhiSS Preliminary Results
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30 40 50 60 70 80
Ph
iSS s
Nb of Recordings
PGA
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40 50 60 70 80
Ph
iSS s
Nb of Recordings
T 1 sec
Magnitude Dependence: CA
22
0
0.1
0.2
0.3
0.4
0.5
0.6
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Ph
iSS
Mag
PGA
0
0.1
0.2
0.3
0.4
0.5
0.6
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Ph
iSS
Mag
T 1.0 sec
Distance Dependence: CA
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200 250
Ph
iSS
Rrup (km)
PGA
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200 250
Ph
iSS
Rrup (km)
T 1.0 sec
M-R Dependence: CA
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0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250
Ph
iSS
Rrup (km)
PGA
M 3 to 5 M 5 to 6 M 6 to 8
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250
Ph
iSS
Rrup (km)
T 1.0 sec
M 3 to 5 M 5 to 6 M 6 to 8
VS30 Dependence: CA
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
100 300 500 700 900 1100 1300
Ph
iSS
Vs30 (m/sec)
PGA
0
0.1
0.2
0.3
0.4
0.5
0.6
100 300 500 700 900 1100 1300
Ph
iSS
Vs30 (m/sec)
T 1.0 sec
References (I)
• Al Atik, L., N. Abrahamson, J. Bommer, F. Scherbaum, F. Cotton, N., Kuehn (2010). The variability of ground-motion prediction models and its components, Seism. Res. Let., 81(5), 794-801.
• Bommer, J. J. (2010). Sigma: What it is, why it matters and what we can do with it, NGA-East workshop presentation, February 10, 2010.
• Strasser, F.O., N.A. Abrahamson and J.J. Bommer (2009). Sigma: Issues, insights and challenges, Seism. Res. Let., 80(1), 40-54.
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